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Equation 114 · Part 2 · The Bend an Elevator Cannot Fake

Symbol Phi_,ij

Tij→Φ,ij\mathcal T_{ij} \to \Phi_{,ij}
Φ,ij\Phi_{,ij}

What this part means

Phi_,ij is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

Its job in the formula

Phi_,ij is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

The passage around this formula

…Second, weak-field gravity: expanding ϕ\phi ≈\approx Φ\Phi/c2c^2 for small Φ\Phi/c2c^2 , the quadratic term ϕ,i\phi_{,i}ϕ,j\phi_{,j} is second order in the already-small ratio Φ\Phi/c2c^2 and negligible next to the first-order term ϕ,ij\phi_{,ij} ≈\approx Φ,ij\Phi_{,ij}/c2c^2 , so Tij\mathcal T_{ij} →\to Φ,ij\Phi_{,ij} , exactly the ordinary Newtonian tidal tensor of tower and satellite geodesy [ 15 , 14 ] . The first derivative alone, meanwhile, recovers the textbook gravitational redshift these networks were already built to measure: y…

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